Calculating the Mass of One Molecule of CO and CO?: A Comprehensive Guide

Introduction to Molecules and Atomic Mass

Understanding the mass of a single molecule of a compound is essential in various scientific fields such as chemistry and biochemistry. This article will provide a step-by-step guide on how to determine the mass of one molecule of carbon monoxide (CO) and carbon dioxide (CO?) using the principles of atomic and molecular mass, Avogadro's number, and molar mass.

Calculating the Mass of One Molecule of CO

The molecular formula for carbon monoxide (CO) is simple, consisting of one carbon (C) atom and one oxygen (O) atom. To calculate the mass of one molecule of CO, we first need to find its molar mass and then convert it to the mass of one molecule.

Step 1: Find the Molar Mass of CO

The atomic weight of carbon (C) is approximately 12.01 g/mol, and the atomic weight of oxygen (O) is approximately 16.00 g/mol. To find the molar mass of CO, we sum these values:

[text{Molar Mass of CO} 12.01 , text{g/mol} 16.00 , text{g/mol} 28.01 , text{g/mol}]

Step 2: Convert Molar Mass to the Mass of One Molecule

One mole of any substance contains Avogadro's number, which is approximately (6.022 times 10^{23}) molecules/mol. To find the mass of one molecule, we divide the molar mass by Avogadro's number:

[text{Mass of one CO molecule} frac{28.01 , text{g/mol}}{6.022 times 10^{23} , text{molecules/mol}} approx 4.65 times 10^{-22} , text{g}]

Thus, the mass of one molecule of CO is approximately (4.65 times 10^{-22}) grams.

Calculating the Mass of One Molecule of CO?

Now, let's move on to carbon dioxide (CO?), which has a more complex molecular formula consisting of one carbon atom covalently bonded to two oxygen atoms. The molecular mass of CO? can be calculated as follows:

Step 1: Find the Molecular Mass of CO?

To find the molecular mass of CO?, we sum the atomic weights of the constituent atoms:

[text{Molecular Mass of CO}_2 12 , text{amu (atomic mass units)} times 1 16 , text{amu} times 2 44 , text{amug}]

Step 2: Convert Molecular Mass to Molar Mass

The molar mass of CO? is the mass of one mole of CO? molecules, measured in grams per mole (g/mol). Since one mole of CO? has (6.022 times 10^{23}) molecules, the molar mass (in grams) is equal to the molecular mass (in atomic mass units):

[text{Molar Mass of CO}_2 44 , text{g/mol}]

Step 3: Calculate the Mass of One CO? Molecule

To find the mass of one molecule of CO?, we divide its molar mass by Avogadro's number:

[text{Mass of one CO}_2 , text{molecule} frac{44 , text{g/mol}}{6.022 times 10^{23} , text{molecules/mol}} approx 7.306 times 10^{-23} , text{g}]

Thus, the mass of one molecule of CO? is approximately (7.31 times 10^{-23}) grams.

Conclusion

Understanding the mass of a single molecule is crucial for various scientific and engineering applications. By following these steps and using the principles of atomic and molecular mass, we can accurately determine the mass of one molecule of CO and CO?.

Key Points

The mass of one molecule of a compound is determined by dividing the molar mass by Avogadro's number. Carbon monoxide (CO) has a molar mass of 28.01 g/mol, and one molecule weighs approximately (4.65 times 10^{-22}) grams. Carbon dioxide (CO?) has a molar mass of 44 g/mol, and one molecule weighs approximately (7.31 times 10^{-23}) grams. Avogadro's number, (6.022 times 10^{23}), is a constant used to relate the amount of a substance to its constituent atoms or molecules.

References

1. "Molecular Mass and Atomic Mass". National Institute of Standards and Technology (NIST), 2. "Avogadro's Number". Britannica,